The iron-based superconductors[1]}, [2]}, [3]} represent the second class of high temperature superconductors after the first discovery of high temperature superconductivity in cuprates[4]}. The electronic structure of the iron-based compounds usually consists of hole-like bands near the Brillouin zone center and electron-like bands near the Brillouin zone corners, leading to proposals that the electron scattering between the hole pockets around the Brillouin zone center and the electron pockets around the Brillouin zone corners is a viable mechanism for electron pairing in the iron-based superconductors[5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. With the discovery of the A\(_x\) Fe\(_{2-y}\) Se\(_2\)  (A=K, Cs, Rb, Tl and etc.) superconductors[12]}, [13]}, [14]}, [3]}, such a Fermi surface nesting picture is challenged because the superconducting phase in A\(_x\) Fe\(_{2-y}\) Se\(_2\)  superconductors does not contain hole pockets near the Brillouin zone center[16]}, [17]}, [18]}, [19]}, [14]}, [3]}. The latest discovery of possible high temperature superconductivity above 65 K in the single-layer FeSe film grown on the SrTiO\(_3\)  substrate (denoted as FeSe/SrTiO\(_3\)  film hereafter) puts even stronger constraints on the Fermi surface nesting picture because there is no Fermi surface present near the zone center at all[22]}, [23]}, [24]}, [25]}, [26]}. While the implications of the Fermi surface topology in the A\(_x\) Fe\(_{2-y}\) Se\(_2\)  superconductors and superconducting single-layer FeSe/SrTiO\(_3\)  films are significant, the material-specific complications make the conclusion on the role of Fermi surface topology ambiguous. The A\(_x\) Fe\(_{2-y}\) Se\(_2\)  superconductors are well-known to have problems of inhomogeneity, phase separation and small superconducting volume fraction. The exact nature of the superconducting phase remains unclear, and its coexistence with the insulating phase suggests that interface may play an important role in the superconductivity[27]}, [28]}, [29]}, [30]}. There are strong indications that interface in the single-layer FeSe/SrTiO\(_3\)  films plays an important role in giving rise to high temperature superconductivity[22]}, [23]}, [24]}, [25]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, [41]}, [26]}. With the complications of the interface effect and phase separation problem involved in A\(_x\) Fe\(_{2-y}\) Se\(_2\)  superconductors and superconducting single-layer FeSe/SrTiO\(_3\)  films, it becomes less straightforward to conclude whether the same effect of Fermi surface topology on superconductivity is operative in all the iron-based superconductors.
